Treasury Securities - Weatherhead

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Treasury Securities

In this chapter we will learn about ? Treasury Bills, ? Treasury Notes and Bonds, ? Strips, ? Treasury Inflation Protected Securities, ? and a few other products including Eurodollar deposits. The primary focus is on the price conventions in these markets. We also

will investigate arbitrage restrictions that exist between strips and coupon bonds.

Debt issued by the Treasury with maturities of one year or less are issued as discounted securities called Treasury bills (T-Bills). Securities with maturities greater than a year are coupon securities. Coupon securities with maturities less (greater) than 10 years are called Treasury notes (bonds).

2.1 TREASURY BILLS

A Treasury bill is a zero coupon bond with a maturity of less than one year. Treasury bills are issued in increments of $5, 000 above a minimum amount

15

16 CHAPTER 2: TREASURY SECURITIES

of $10, 000. Over $200 billion are issued per year. T-bills are unusual in that their prices are not directly quoted. The Wall Street Journal, for example, ranks T-bills by maturity. The maturity date is followed by "prices" expressed in bank discount yield form, dy, where:

F - B 360

dy =

F

? m

where m - number of days to maturity F - Face value of the Bill B - Price of the Bill.

Given the discount yield, the invoice price is given by:

B = F ? [1 - m ? dy ] 360

For example, if the bank discount yield is 6.78%, and the maturity is 160 days, then the price per $100 of face value is:

160 ? 0.0678

B = 100 ? [1 -

] = 96.98667

360

The discount yield divides the dollar gain by the face value and so is not a good indicator of return. In addition, the discount is based on a 360 day year. The difference between the bid and asked discount yield is the profit margin of the dealer. The bid ask spread is usually very small, perhaps two basis points.

In order to make yields of T-Bills comparable to yields of other types

of coupon bonds, namely T-Notes and T-Bonds, market participants often

compute the Bond Equivalent Yield (BEY) of the investment. The BEY not

only correct the shortcommings of the bank discount yield but also attempts to

set up a yield measure which is comparable to yield measures of coupon bonds

with semi annual payments based on a 365 day year. The bond equivalent

yield is given by:

(100 - B) 365

BEY =

?

B

m

The reported BEY is based on the ask discount quotes.

Actually, the market convention for computing a BEY for a T-Bill with m > 182 days is more complex. Market convention attempts to establish a bond equivalent yield for this T-Bill so that comparisons can be made with other bonds that pay coupons semi-annually. To establish this value we pretend interest of y is paid after 6 months and that it is possible to reinvest this interest for the remaining time to maturity. Hence, begining with B dollars, after six months we would have B(1 + y/2). Over the remaining n = (m - 365/2) days this value is assumed to grow to B(1+y/2)(1+n?y/365). Setting

CHAPTER 2: TREASURY BILLS 17

this value to the face value and solving for y leads to the BEY. Hence:1

y

y

B(1 + )[1 + n ? ] = F

2

365

Table 2.1 displays typical T-Bill prices quotations as reported in the financial press.

Table 2.1 Selected T-Bill Price Quotations on January 4th 1999

Maturity Date Days to Mat. Bid Ask Ask Yield

Jan 14 99

9

Jan 21 99

16

Jan 28 99

23

3.92 3.84 3.90 4.53 4.45 4.52 4.38 4.30 4.37

April 1 99

86

April 8 99

93

July 1 99

177

Dec 9 99

338

Jan 6 00

366

4.44 4.43 4.54 4.42 4.40 4.51 4.38 4.37 4.54 4.39 4.38 4.58 4.33 4.32 4.53

Consider the April 1 99 T-Bills, with 86 days to maturity. The asked

discount yield is 4.43. This implies the cost per $100 face value is 100 ? [1 -

86?0.043 360

]

=

$98.94172.

The

bond

equivalent

yield

is

4.54%,

and

is

indicated

in the last column.

Example

Consider a 13-week $10, 000 face value T-bill with an asked discount yield of 8.88%.

? The cost of this bond is B = F [1 - (m/360)dy] = 10, 000[1 - (91/360)0.0888] = $9, 775.53

? The bond equivalent yield is

F - B 365 10, 000 - 9, 775.53 365

?=

? = 9.21%.

B

m

9, 775.53

91

1An alternative formula might require

B(1

+

y/2)1+

2n 365

= 100

but this is not the market convention here!

18 CHAPTER 2: TREASURY SECURITIES

? The effective annual rate of return compounded on a daily basis is [ 10, 000 ]365/91 - 1 = 0.0953 or 9.53% 9, 775.53

? The effective annual rate of return compounded on a continuous basis

is:

10, 000 365

log[

] ? = 0.0911 or 9.11%

9, 775.53 91

2.2 TREASURY NOTES AND BONDS

T-bills are short term instruments that pay no coupons prior to maturity. We now turn attention to coupon bonds issued by the treasury. All treasury bonds are identified by their coupon and maturity. The 101/2 of 1999 means the Treasury bond with a 10 1/2% annual coupon rate that matures in 1999. The dollar amount of interest paid per year is 101/2% of the face value. In practice the coupon are paid in two equal installments, six months apart.

Quotations for Treasury notes and Treasury bonds are usually reported together, ordered by maturity. The bid and ask prices are reported in a special form. For example a quotation of 86 - 12 means the price is 86 12/32% of face value. A plus sign following the the number of 32nds means that a 64th is added to the price. To actually purchase a bond, the investor must pay the asked price together with accrued interest since the last coupon payment. Accrued interest is computed by taking the size of the last coupon payment and multiplying by the ratio of the actual number of days since the last coupon payment, relative to the actual number of days in the coupon period.

Table 2.2 illustrates typical price quotations of selected notes and bonds.

As an example, consider the November 2008 Treasury note with coupon 4 3/4. The "n" indicates the contract is a note rather than a bond. The bid quotation price is 100 16/32 and the ask quotation price is 100 17/32. Interest payments are semiannual on the 15th of November and 15th May. The ask invoice price is the asking quotation price plus the accrued interest. Using this price the yield to maturity is computed as 4.68%.

Some T-bonds are callable, with the first-call date coming 5 years before the bond matures. Newspaper quotations typically indicate if the bond has a call feature. For callable bonds, the yield to maturity is reported if the price is below par. If the price is above par, then the yield to the call date is computed. Over the last decade, however, the auctions have not included callable Treasury securities, so the number of such contracts is diminishing.

CHAPTER 2: TREASURY NOTES AND BONDS 19

Table 2.2 Selected Note and Bond Price Quotations for Settlement on January 6th 1999

Rate Maturity (Mo/Yr) Bid Price Ask Price Ask Yield

6 3/8 5 5 7/8 5 8 7/8

Jan 99n Jan 99n Jan 99 Feb 99n Feb 99n

100:00

100:02

3.95

99:31

100:01

4.46

100:01

100:03

4.43

100:00

100:02

4.35

100:13

100:15

4.49

7 1/8 4 5/8 6 1/4 4 1/4 4 3/4 8 1/8 5 1/4

Feb 00n Dec 00n Feb 02n Nov 03n Nov 08n Aug 21 Nov 28

102:19

102:21

4.72

100:02

100:03

4.5

104:10

104:12

4.74

98:20

98:21

4.56

100:16

100:17

4.68

134:12

134:18

5.45

101:16

101:17

5.15

Viewed from a coupon date, and including the date 0 coupon, the yield-tomaturity of a Treasury bond is linked to its market price by the usual bond pricing equation:

m-1 C/2

100 + C/2

B0 =

(1 + y/2)j + (1 + y/2)m

j=0

where 100y% is the annual yield to maturity, C is the annual coupon rate and m is the number of coupon payouts remaining to maturity.

If, however, the time to the first coupon date is not exactly 6 months, then

the bond pricing equation must be modified. Specifically, the pricing equation

is given by

B0

=

1 (1 + y/2)p

m-1

C/2 (1 + y/2)j

+

100 (1 + y/2)m-1

j=0

where p = tn/tb and tn is the number of days to the next coupon payment, and tb is the number of days from the last coupon date to the next coupon date.

The price that an investor pays is the quoted price, together with the accrued interest. The accrued interest, AI say, equals the proportion of the current coupon period that has elapsed, times the coupon size. That is:

AI = [1 - p]C/2

20 CHAPTER 2: TREASURY SECURITIES

and B0 = Q0 + AI

where Q0 is the quoted bond price. The total price paid for a bond is often referred to as the full price or

dirty price while the quoted price is often called the flat price or clean price

Example (i) Consider a T-bond with a 10% coupon which pays out 20 more coupons.

The time from the last to the next coupon date, tb, is 183 days. Since the last coupon was paid 83 days before the settlement date, the time to the next coupon, tn , is 100 days. The quoted price for the bond, Q, based on $100 face value is 104 : 08. In decimal form the price is 104 8/32 = $104.25. To obtain the market price, B0, the accrued interest must be added. Since the last coupon was paid 83 days ago, the accrued interest per $100 face value, AI, is given by

AI = [83/183] ? 5 = $2.26775

The actual market price for the bond is its quoted price plus accrued interest. That is

B0 = 104.25 + 2.26775 = $106.51775. The yield to maturity, y, is obtained by solving the yield in the bond pricing equation.

(ii) Consider the Feb 2000 T-note that pays a 7 1/8 coupon in the table above. The quoted price is 102 21/32 = $102.656. There is 183 days in this coupon interval and there are 39 days remaining till the next coupon is paid. The previous owner is entitled to 183-39 = 144 days of interest. The accrued interest is

144 AI = 3.5625 ? = $2.803

183

The market price of the bond is therefore $105.459. Plugging this value into the left hand side of the bond pricing equation, and solving for the bond equivalent yield provides the answer of 4.72%.

Settlement Dates

The trade date is the date when parties agree on a price and promise to transact, and the settlement date is the date when money and bonds change hands. Treasury bonds usually settle "next day", or one business day after the trade date. While this is the normal procedure, the actual time to settlement can be negotiated between buyer and seller.

CHAPTER 2: STRIPPED COUPON BONDS 21

The accrued interest is based from the settlement date, not the trade date. The first day of accrued interest is therefore the day after the settlement date. Hence, if the bond settles on a coupon date, the seller gets the full coupon.

2.3 STRIPPED COUPON BONDS

Consider an investor with a one year holding horizon. If the investor purchase a 2 year zero coupon bond, then after one year, the investor has to sell the bond at a price which will depend on interest rates in one years time. The investment has price risk. If the investor purchased a one year zero coupon bond, then the strategy is absolutely riskless. The investor will receive the face value in one year, regardless of interest rates. Finally, if the investor purchased a six month T-Bill, with the intent of rolling this investment over into a new 6 month investment, then the return over the year would depend on the reinvestment rate after 6 months. This strategy has reinvestment risk.

Zero coupon bonds are attractive investments for investors such as pension funds and insurance companies who have fixed obligations in the future and want to ensure that these obligations will be met regardless of future interest rates. Zero coupon bonds permit terminal values to be locked in at known rates of return without incurring price and reinvestment risk. Given the likelihood of sizable demand for zeros by pension funds and insurance firms, for example, it is somewhat surprising that such few zeros have been issued. Indeed, apart from short term Treasury Bills, the US Treasury has not issued any zeros.

Financial intermediaries do construct securities which resemble zero coupon debt. Beginning in 1982, the practice of stripping US Treasury securities developed. The first two big strippers were Merrill Lynch, who created TIGRS (Treasury Investment Growth Receipts) and Salomon Bros. who created CATS (Certificates of Accrual on Treasury Receipts). These firms, would purchase Treasury bonds, place them in trust, and then sell claims on the individual cash flows. If a 10 year bond with 20 semi-annual coupons is stripped, the underlying bond is resold as 21 zeros (20 coupons and a principal strip) each of which trades separately in the securities market. In a perfect market, the portfolio of the individual strips has the same value as the whole bond. Differences in values could occur if tax treatments were different. Indeed, the creation of this product by Merrill Lynch and Salomon was primarily motivated by the favorable tax treatment of strips, and the perception that there was an unsatisfied clientele who demanded zeros, and who were prepared to pay a premium for them.

In practice, the cost of stripping and reselling the packages of zeros was quite high. First, trust accounts had to be set up. Second, buyers for the strips had to be found. Third, interest rate risk over the interim period had

22 CHAPTER 2: TREASURY SECURITIES

to be hedged. In order to reduce these costs and expedite stripping, in 1985, the US Treasury designated some Treasury securities eligible to be stripped through the Federal Reserve book entry system. The resulting zero coupon bonds, called STRIPS (Separate Trading of Registered Interest and Principal of Securities) now dominate this market because it is the least costly form of stripping.

As an example assume the date is January 4th and that a financial institution is holding a 100,000 dollar face value T-note that pays 5% coupons and matures in two years. This bond will pay $2500 in January 15th and July 15th of this year and the next, as well as the terminal 100,000 dollars. If this bond is delivered to the Treasury to be stripped, then five Strips will be created. The first four strips, each having a face value of 2500 dollars, are called coupon strips or C-strips, while the 100, 000 dollar two year strip, with maturity on July 15th of next year, is called a principal strip or P-strip. Each of these strips are assigned a CUSIP number and can trade separately.

Institutions are allowed to unbundle or reconstitute these bonds. For example, an investor could deliver these five strips to the Treasury and request that the original 5% coupon bond be reconstituted. Actually, in reconstituting a bond, any C-strips can be used for the coupon payments, but the principal payments must come from the appropriate P-strip. That is C-strips are completely fungible, but P-strips are not. Specifically, any particular P-strip can only be used to reconstitute a particular bond.

Table 2.3 shows selected prices of STRIPS on January 4th 1999.

There are three types of STRIPS. Stripped coupon interest (ci), treasury bond stripped pricipal (bp) and treasury note stripped principal (np). Principal strips and interest strips may differ by a small amount. However, arbitrage forces ensure that they do not differ by enough to make purchasing the cheaper and selling the expensive profitable.2

A plot of the strip prices, with face values equal to one dollar, against maturity yields a graph that should be a decreasing function, starting from one (at date 0) and declining towards zero. This information is very useful for establishing a discount function, but is not the only set of data that provides information on discount factors. Clearly, T-Bill information adds to the information set. Also, coupon bonds provide information on discount factors. We will explore methods for estimating and constructing a reliable discount function in a later chapter.

Example

2A distinction is made between STRIPS created from coupons and principal because of tax treatments by non US entities.

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